Steel rods are manufactured with a mean length of 25 centimeters (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed, with a standard deviation of 0.07 cm. Any rods that are shorter than 24.85 cm or longer than 25.15 cm are discarded. What proportion of rods will be discarded

3.24% of rods will be discarded

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What proportion of rods will be discarded

Shorter than 24.85.

pvalue of Z when X = 24.85

has a pvalue of 0.0162

Longer than 25.15

1 subtracted by the pvalue of Z when X = 25.15

has a pvalue of 0.9838

1 - 0.9838 = 0.0162

2*0.0162 = 0.0324

3.24% of rods will be discarded

The proportion of rods will be discarded is 0.03236

Step-by-step explanation:

From the question;

mean; μ = 25 cm

Standard deviation; σ = 0.07 cm)

Now, this is a normal distribution problem where we are supposed to find the Z-score.

Z is given by;

Z = (X - μ)/0.07

Applying this to the question of, rods that are shorter than 24.85 cm or longer than 25.15 cm are discarded. We arrive at;

P(X<24.85) + P(X>25.15)

This will give us;

P(z < [(24.85 - 25)/0.07)]) + P(z > [(25.15 - 25)/0.07)])

= P(z < (-2.143)) + P(z > 2.14)

This now transforms to;

= P(z ≤ (-2.143)) + 1 - P(z ≤ 2.143)

From standard normal table which i have attached,

P(z ≤ (-2.143)) = 0.01618 and

P(z ≤ 2.143) = 0.98382

Thus,

P(X<24.85) + P(X>25.15) = 0.01618 + 1 - 0.98382 = 0.03236

black lol

step-by-step explanation:

h

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this made me lol.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕